Spectral Structures and Topological Methods in Mathematics (EMS of Congress Reports) - Hardcover

Michael Baake

Hardcover

ISBN 10: 303719197X ISBN 13: 9783037191972

Publisher: European Mathematical Society, 2019

Synopsis

This book is a collection of survey articles about spectral structures and the application of topological methods bridging different mathematical disciplines, from pure to applied. The topics are based on work done in the Collaborative Research Centre (SFB) 701. Notable examples are non-crossing partitions, which connect representation theory, braid groups, non-commutative probability, as well as spectral distributions of random matrices. The local distributions of such spectra are universal and also represent the local distribution of zeros of L-functions in number theory. An overarching method is the use of zeta functions in the asymptotic counting of sublattices, group representations, etc. Further examples connecting probability, analysis, dynamical systems, and geometry are generating operators of deterministic or stochastic processes, stochastic differential equations, and fractals, relating them to the local geometry of such spaces and the convergence to stable and semi-stable states.

Edition details

• Publisher: European Mathematical Society
• Publication date: 2019
• Language: English
• ISBN 10: 303719197X
• ISBN 13: 9783037191972
• Binding: Hardcover
• Edition number: 1
• Number of pages: 433
• Editor: Michael Baake, Friedrich Gotze, Werner Hoffmann